<header>
    基本概念与性质
</header>
<p>
    <span class="title">
        定义
    </span>
    设Ω为一个样本空间，ℱ为Ω的某些子集组成的一个事件域。如果对任一事件A∈ℱ，定义在ℱ上的一个实值函数P(A)满足：
</p>
<ol>
    <li>
        <span class="important">非负性公理</span> 若A∈ℱ，则P(A)≥0
    </li>
    <li>
        <span class="important">正则性公理</span> P(Ω)=1
    </li>
    <li>
        <span class="important">可列可加性公理</span> 若A<sub>1</sub>，A<sub>2</sub>，...，A<sub>n</sub>，...互不相容，则
    </li>
</ol>
<p>
    <code>
        ["join","p",["bracket",["join",["listedOr","i=1","∞"],["rightBottom","A","i"]],"small"],"=",["sum","i=1","∞",["join","P(",["rightBottom","A","i"],")"]]]
    </code>
</p>
<p>
    则称P(A)为事件A的<span class="important">概率</span>，称三元素（Ω，ℱ，P）为<span class="important">概率空间</span>。
</p>
<h2>
    常用性质
</h2>
<p>
    <span class="title">
        性质（有限可加性）
    </span>
    若有限个事件A<sub>1</sub>,A<sub>2</sub>,...,A<sub>n</sub>互不相容，则有
    <span class="oneline">
        <code>
            ["join","p",["bracket",["join",["listedOr","i=1","n"],["rightBottom","A","i"]],"small"],"=",["sum","i=1","n",["join","P(",["rightBottom","A","i"],")"]]]
        </code>
    </span>
</p>
<p>
    <span class="title">
        性质
    </span>
    若A⊃B，则
    <span class="oneline">
        P(A-B) = p(A) - P(B)
    </span>
</p>
<p>
    <span class="title">
        性质（加法公式）
    </span>
    对任意两个事件A,B，有
    <span class="oneline">
        P(A∪B) = P(A) + P(B) - P(AB)
    </span>
    对任意n个事件A<sub>1</sub>,A<sub>2</sub>,...,A<sub>n</sub>，有
    <span class="oneline">
        <code>
            ["join",
                "p",["bracket",["join",["listedOr","i=1","n"],["rightBottom","A","i"]],"small"],"=",
                ["sum","i=1","n",["join","P(",["rightBottom","A","i"],")"]],"-",
                ["sum","1≤i＜j≤n","",["join","P(",["rightBottom","A","i"],")","P(",["rightBottom","A","j"],")"]],"+",
                ["sum","1≤i＜j＜k≤n","",["join","P(",["rightBottom","A","i"],")","P(",["rightBottom","A","j"],")","P(",["rightBottom","A","k"],")"]]
            ]
        </code><br />
        + ... + (-1)<sup>n-1</sup>P(A<sub>1</sub>A<sub>2</sub>...A<sub>n</sub>)
    </span>
</p>